21:39 Jul 1, 2020 |
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German to English translations [PRO] Tech/Engineering - Automation & Robotics / conveyor belts / servo motors / automation | |||||||
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Summary of answers provided | ||||
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4 +1 | converges on its final position S0 at a quadratic rate |
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3 +1 | gravitate / edge in non-linear least squares towards an end-value |
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4 | tends quadratically towards |
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Summary of reference entries provided | |||
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Quadratic convergence |
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Discussion entries: 5 | |
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strebt quadratisch gegen ihren Endwert s0. converges on its final position S0 at a quadratic rate Explanation: I asked a mathematician, Cilian. Sometimes, you have to go beyond the talent pool on Kudoz. |
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quadratisch gegen einen Endwert streben gravitate / edge in non-linear least squares towards an end-value Explanation: I doubt this is anything to do with square roots or 'quadratic equations' from my school days last millennium, rather a parallel with linear / straight-line vs. reducing or declining balance 'squared' depreciation in accounting. FWIW, I - having read works by a cousin once teaching at the technische Universität in Vienna - can't see anything wrong with the German, but maybe someone else can. Example sentence(s):
Reference: http://eng.proz.com/personal-glossaries/entry/2717023-kleins... Reference: http://www.roboticsproceedings.org/rss09/p42.pdf |
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tends quadratically towards Explanation: it's a standard mathematical phrase, just like "tends asymptotically to" (Calculus) it moves towards that point in the fashion of a quadratic function (x to the power of 2). I don't think there's much need to overthink this one. It appears like this in dozens of books, just see Google Books for instance. -------------------------------------------------- Note added at 1 day 8 hrs (2020-07-03 06:35:19 GMT) -------------------------------------------------- A Google search on my computer got 368.000 results. "Dozens" were just the books listed on the first results page, which include this exact phrase. See for instance: Foundations of Computational Mathematics (Minneapolis, 2002) - page 122. Or Geometric Computations with Interval and New Robust Methods - page 50. -------------------------------------------------- Note added at 1 day 9 hrs (2020-07-03 06:53:01 GMT) -------------------------------------------------- Additional references: https://math.stackexchange.com/search?q=tend towards to https://math.stackexchange.com/questions/1735193/in-practice... So basically, they converge or tend (if a function has limits, it tends to the limits; else it converges)... -------------------------------------------------- Note added at 1 day 9 hrs (2020-07-03 07:03:11 GMT) -------------------------------------------------- http://sepwww.stanford.edu/public/docs/sep97/paul1/paper_htm... -------------------------------------------------- Note added at 1 day 16 hrs (2020-07-03 14:33:59 GMT) -------------------------------------------------- I typed "tends quadratically to". I admit I only looked at the first page. There I get a list of 6 books (GoogleBooks) that contain this exact phrase - they all deal with advanced mathematics of some kind. The remaining hits are probably due to the "tends to", which is quite common, so you are right, they are not relevant. I wish I could send you a screenshot. (It doesn't mean that my answer is correct, of course. My husband is an automotive engineer and he likes Lancashireman's answer best.) -------------------------------------------------- Note added at 1 day 17 hrs (2020-07-03 15:13:40 GMT) -------------------------------------------------- See also: http://www.netlib.org/utk/people/JackDongarra/PAPERS/Improvi... https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/200... https://arxiv.org/pdf/1704.06106.pdf (page 10) https://core.ac.uk/download/pdf/25212689.pdf Again, not sure if these apply to your specialism, but I have now double-checked and there are at least 4-5 results pages in Google for the phrase "tends quadratically to" (not towards!) Reference: http://https://books.google.de/books?id=3MQFkk12PBcC&pg=PA15... Reference: http://https://books.google.de/books?id=VLWkAgAAQBAJ&pg=PA50... |
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2 hrs peer agreement (net): +2 |
Reference: Quadratic convergence Reference information: https://bookdown.org/rdpeng/advstatcomp/rates-of-convergence... Quadratic Convergence Quadratic convergence is the fastest form of convergence that we will discuss here and is generally considered desirable if possible to achieve. We say the sequence converges at a quadratic rate if there exists some constant 0 -------------------------------------------------- Note added at 2 hrs (2020-07-02 00:29:18 GMT) -------------------------------------------------- ... Extending the examples from above, the sequence xn=1+(1n)2n converges quadratically to 1. .... -------------------------------------------------- Note added at 4 hrs (2020-07-02 01:48:15 GMT) -------------------------------------------------- ungleichmäßige versus lineare Beschleunigung: https://studyflix.de/ingenieurwissenschaften/beschleunigung-... gradual (quadratic) acceleration: https://www.vexforum.com/t/gradual-quadratic-acceleration/22... non-linear (quadratic) function: https://ui.adsabs.harvard.edu/abs/2016EGUGA..1816816B/abstra... It is clear that not all GNSS position time series follow this simple linear behaviour. Therefore, we have added an acceleration term in the form of a quadratic polynomial function to the model in order to better describe the non-linear motion in the position time series. |
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